Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations

Full text

Pdf (547 KB)

Source

Journal of the ACM (JACM) archive
Volume 26 , Issue 3 (July 1979) table of contents

Pages: 483 - 493

Year of Publication: 1979

ISSN:0004-5411

Author

T. D. Bui

Department of Computer Science, Sir George Williams Campus, Concordia University, 1455 de Maisonneuve Blvd West, Montreal, Quebec H3G 1M8, Canada

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 9, Downloads (12 Months): 68, Citation Count: 2

Additional Information:

references cited by index terms collaborative colleagues peer to peer

Tools and Actions:	Review this Article Save this Article to a Binder Display Formats: BibTex EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/322139.322147 What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ALLEN, R H, AND POTTLE, C Stable integration methods for electronic orcutt analysis with widely separated time constants, Proc Sixth Annual Allerton Conf on Clrcult and System Theory, U of llhnots at Urbana- Champaign, Urbana, I11, T Trick and R T Chlen, Eds, 1966, pp 311-320
	2	BICKART, T A An efficient solution process for implicit Runge-Kutta methods SIAM d Numer Anal 14, 6 (Dec 1977), 1022-1027
	3	BRANDON, D M A new single-step implicit integration algorithm with A-stablhty and improved accuracy S:mulat:on 23, 1 (July 1974), 17-29
	4	T. D. Bui, Errata and Comments on a Paper by J. R. Cash, Journal of the ACM (JACM), v.24 n.4, p.623, Oct. 1977 [doi>10.1145/322033.322040]
	5	Btsr, T D, AND GHADERPANAH, S Modified Richardson extrapolation scheme for error estimate in tmphcit Runge-Kutta procedures for stiff systems of ordinary differential equations Proc Seventh Manitoba Conf on Numerical Math and Comptng, Utlhtas Mathematlca Pub, lnc, Winnipeg, Mamtoba, Canada, 1977, pp 251-268
	6	BuI, T D, LELrNG, K V, AND BuI, T R New developments in computer techniques for stiff differential equations Proc Sixth Canadian Congress of Appl Mech, U of British Columbia, Vancouver, Brmsh Columbia, Canada, 1977, pp 1035-1037
	7	BURRAGE, K A special family of methods for solving surf differential equations Res Rep No I10, Dept of Mathematics, U of Auckland, Auckland, New Zealand, May 1977
	8	BUTCHER, J C Imphot Runge-Kutta processes Math Comput 18 (1964), 50-64
	9	BUTCHER, J C On the lmplementauon of lmphcit Runge-Kutta methods BIT 16 (1976), 237-240
	10	CALAHAN, D A stable accurate method for the numerical integration of nonhnear systems Proc IEEE 56 (April 1968), 744
	11	J. R. Cash, Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations, Journal of the ACM (JACM), v.23 n.3, p.455-460, July 1976 [doi>10.1145/321958.321966]
	12	DAHLQUIST, G G A special stability problem for linear multlstep methods BIT 3 (1963), 27-43
	13	EHLE, B L High order A-stable methods for the numerical solution of differential equations BIT 8 (1968), 276-278
	14	HAINES, C F Imphclt integration processes wRh error estimates for the numerical solution of differential equations Computer J 12 (1968), 183-187
	15	LAMBERT, J D Computational Methods tn Ordinary D~fferenttal Equations Wiley, New York, 1973
	16	LINDBERG, B On smoothmg and extrapolation for the trapezoidal rule BIT 11 (1971), 29-52
	17	NORSETT, S P Semi-explicit Runge-Kutta methods Math and Computation Rep 6/74, Dept of Math., U of Trondhelm, Trondheim, Norway, 1974
	18	PICEL, Z Block one-step methods with free parameters for numerical integration ofstlffordmary differential equattons Ph D Th, Syracuse U, Syracuse, N Y. 1975
	19	ROSENaROCK, H H Some general ~mpllctt processes for the numerical solution of differential equations Computer J 5 (1963), 329-330
	20	WOLFBRANDT, A A study of Rosenbrock processes w~th respect to order condmons and st~ff stabdtty Res Rep No 77 01, Dept of Comptr Sc~, U of Goteborg, Goteborg, Sweden, 1977

CITED BY 2

	J. R. Cash , S. Considine, An MEBDF code for stiff initial value problems, ACM Transactions on Mathematical Software (TOMS), v.18 n.2, p.142-155, June 1992
	L. F. Shampine, Implementation of Rosenbrock Methods, ACM Transactions on Mathematical Software (TOMS), v.8 n.2, p.93-113, June 1982

INDEX TERMS

Primary Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.7 Ordinary Differential Equations
Subjects: Stiff equations

General Terms:
Measurement, Performance, Reliability, Theory

Collaborative Colleagues:

T. D. Bui: colleagues

Peer to Peer - Readers of this Article have also read:

Interactive skeleton-driven dynamic deformations ACM Transactions on Graphics (TOG) 21, 3
Steve Capell , Seth Green , Brian Curless , Tom Duchamp , Zoran Popović
Data structures for quadtree approximation and compression Communications of the ACM 28, 9
Hanan Samet
A hierarchical single-key-lock access control using the Chinese remainder theorem Proceedings of the 1992 ACM/SIGAPP Symposium on Applied computing
Kim S. Lee , Huizhu Lu , D. D. Fisher
The GemStone object database management system Communications of the ACM 34, 10
Paul Butterworth , Allen Otis , Jacob Stein
Putting innovation to work: adoption strategies for multimedia communication systems Communications of the ACM 34, 12
Ellen Francik , Susan Ehrlich Rudman , Donna Cooper , Stephen Levine

Adobe Acrobat

QuickTime

Windows Media Player

Real Player